D'ALEMBERT. 429 



of the Academy, as well as with Sir Martin Folkes, presi- 

 dent of the Royal Society, a sealed paper containing the 

 heads of his analysis, but delayed the publication of it 

 until he should complete the whole to his satisfaction : a 

 most praiseworthy caution, after the error that had been 

 committed in the first instance. He announced, how- 

 ever, the result, and its confirming the Newtonian theory, 

 in May of the same year ; and added, that his reasoning 

 was purely geometrical, and had no reference to vague 

 topics, giving, at the same time, a conclusive exposition 

 of Buffon's ignorance in his hot attack, which showed 

 him to be wholly incapable of appreciating any part of 

 the argument. In May, 1752, the Memoir itself was 

 given to the Academy, and it appears in the volume for 

 1748.* It is entitled, "De TOrbite de la Lune, en ne 

 negligeant pas les quarres des quantites de mme ordre 

 avec les forces perturbatrices ;" which has misled many in 

 their conception of the cause to which the error must be 

 ascribed. But in the volume for 1748, p. 433, he leaves 

 no doubt on that cause ; for he states that having origi- 

 nally taken the radius vector r, (the reciprocal of u in our 



k 



former equation,) = - , he now takes fully 

 1 cos. m v 



that reciprocal u or = 1 - e cos. m v + 13 cos. - 

 r n 



cos. 



7 cos. ( m]v + 8 cos. ( (- m) v f 

 ^ n ' ^n ' 



2 \ 



/- 2 m \ v, terms obtained by the first or trial integra- 

 \n ) 



* For an account of the irregular and irrational manner in which 

 the Memoirs of the Academy were published, see ( Life of Lavoisier.' 

 The inconvenience of it meets us everywhere. 



